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I have a challenge for you. I was on a plane from Denver, my home, to Nashville to visit a college friend. She and I were roommates at a college in Nashville.

I was born in TN and moved to CO at age 23. I was in the center seat on the plane with a man next to me. We did not speak and were caught up in our books/computers/earbuds.

As we were descending into Nashville, we were told that we had to divert due to a weather event. The atmosphere in the cabin changed to something more relaxed, as so often happens when a diversion occurs from what is expected. At this point, this fellow and I began a conversation. I will stress here that if we had landed, said conversation would have never taken place.

The guy was from a city further west from Denver and had made a connection there. He was, at it turns out, flying into Nashville as his final destination, as I was. As we spoke, he told me that he was attending a funeral in a town not too far from Nashville. When asked which town (remember, I am from West TN), he told me the funeral was to be in a tiny town called Selmer. Selmer is actually about a 2 hour drive from Nashville.

I turned to him, astonished. I have an aunt, uncle and cousins who have basically lived in Selmer their whole lives. Wow, what a coincidence! But it gets better.

As we talked, he mentioned that he would be taking the ashes of the deceased to be scattered at a lake nearby, about an hour’s drive from Selmer. When I asked where this would be, I was floored by his answer. The lake and town to which he would be traveling with the ashes was Savannah, TN and Yellow Creek, a dammed area of the Tennessee River.

I graduated high school at Central High School in Savannah in 1981 (i only lived in Savannah for 4 years, mind you) and my extended family owned a small vacation home on Yellow Creek.

Okay, Skepticality, what are the odds?

Below are the extended notes provided by statistician and podcaster Kyle Polich for use in Skepticality Episode 272. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

(Kyle studied computer science followed by artificial intelligence in grad school with a focus in probabilistic reasoning and planning. His general interests range from obvious areas like statistics, machine learning, data viz, and optimization to data provenance, data governance, econometrics, and metrology. He enjoys exploring the intersection of statistics and skepticism and sharing related insights with others including through his podcast Data Skeptic. Visit Kyle’s blog Data Skeptic, and give the podcast a listen.)

Christie’s new acquaintance from the flight happens to mention his destination is the town of Selmer, two hours drive from their landing city of Nashville. He goes on to reference two other small towns, also within two hours of Nashville, to which Christie also has a connection.

Determining just how crazy these odds might be requires an understanding of how connected we are as people. I, for example, live in Los Angeles, California. I know people who live in Santa Monica, Culver City, Hollywood, Monterey Park, La Habra, Studio City, Pacific Palisades… I don’t know anybody from Malibu… anyway, what percentage of towns within two hours drive of me do I have a connection to?

I wrote a program that looks up that list of cities for any input. I generated a list of cities near a few of my friend’s homes and I asked them to tell me which municipalities they had some connection to. From this, I could come up with the frequency that people I know have a connection to cities near them.

To my surprise, I got extremely varied results. Some people had a connection to as few as 5% of nearby cities, while my highest scoring participant claimed to be connected to 70% of nearby municipalities.

Given my wide variety of results, I want to turn the tables on you, the listener. Guess for yourself, what percentage of municipalities within two hours of your home do you have a connection to? 10%? 50%? Think about it, and come up with a percent. Once you’ve got it, imagine you have a coin. But this coin is a weighted trick coin which comes up heads as often as your percent. So if you have few connections to nearby cities, say 1%, then on average, only 1 toss out of 100 is expected to be heads. Hang on to your imaginary coin, we’re going to be flipping that in a minute.

As far as we know, the gentleman in our story called out three cities in a row that Christie had a connection to. This is the equivalent of getting three heads in a row on your imaginary coin. That being the case, we can apply some basic binomial probability to this situation.

If you are connected to only 1% of nearby cities, than your odds are exactly one in a million. But I think that’s extreme. Most people are connected to more cities than that, especially in areas they grew up in. I have a connection to 40% of the cities within 2 hours of where I grew up near Chicago, so for me, the odds of 3 hits in a row are exactly 6.4%. And for anyone connected to only 10% of nearby cities, the odds drop to 0.1%.

So the exact degree of craziness in these odds relies entirely on how connected we are to people in cities that are around us. The less connected we are, the more surprising. I think assuming people are connected to 10% of the places within 2 hours of them sounds conservative and reasonable, so by that frequency, the chances are a bit small at 0.1%, or one chance in a thousand.

When I got home from work this evening and logged onto Facebook, I found out that a friend’s dog, Liam, died today. I had the pleasure of meeting Liam a handful of times, and he was a great dog. He really enriched the lives of many people, not just his own family.

Later in the evening, I found out that the father of another friend of mine died. His name? Liam. I never met this Liam, but his son has been a friend of mine for many years, and he’s someone that I have tremendous respect for, so I’m sure Liam was a great guy and a wonderful father.

I found out about both on Facebook, but both are people that I consider real friends, who I interact with in real life, and not Facebook acquaintances who I’ve only met a few times (or not at all). It’s not often that any of my friends lose a family member or a pet, and even more rare that two of my friends lose a loved one on the same day. I can’t say I recall that happening before, even including on-line only friends, though I’m sure it has. But for two friends to lose loved ones with the same name on the same day? As sad as a coincidence as this is, it’s also kind of amazing.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 271. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

At first glance this sounds like something for which we could calculate odds, and perhaps we could if we knew a few more things, such as the age for the gentleman who died. However, there are a lot of questions to consider. For example, although Liam is not a terribly common name, it can be short for more common names such as William. We also have no way to know how popular the name is for a pet, since there are no birth certificates for the vast majority of pets.

But there is an interesting aspect to this story in that the author found out about these events through Facebook, which has greatly increased the average user’s circle of friends as well as the probability that we will learn about such events in our friends’ lives. So, while it may seem as though tragedy is all around us at times, I think that such coincidences have probably always been common, but we are much more aware of them today as we are much more connected to others.

My wife and I walk our dog every afternoon at nearby trails and parks. My dog loves snow so we often go places that have little traffic in the winter and may not see anyone else during the walk.

Recently we went on a trail and as we were coming back we saw another dog coming down toward us. My dog is small and does not get along well with other dogs so when that happens it is memorable because I usually have to grab him and pick him up until we can assess the situation with the other dog.

In this case the other dog was friendly and was soon followed by her owner who likewise was friendly, so I put my dog down and we all chatted for a few minutes before continuing on our way.

While we had been walking we noticed a trail that we had never been on before, so the next day we went back to the same reservation and went on this other trail, which turned out to be much longer than we anticipated. It met up with the previous trail near the end. So as we came to the exact same spot where we met the dog the day before, bounding down the trail was the same dog again! Since I couldn’t be sure at a distance I had to scoop up my dog again and we reenacted the same scene, in the same place. We chatted with the owner again and went on our way back to the car. What are the odds?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 270. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

The odds of meeting the same dog (with its owner) on the same trail are excellent.

People are creatures of habit, and returning to the same location to walk a dog is not surprising at all. While the second trail was new to the author, he notes that it connected to the trail they had been on the previous day, so it is likely that the other dog owner would choose it, either for the change of view or perhaps because she walks up via one trail and back via the other. The author does not mention the time of day, but I would bet that these events occurred around the same time of day.

Skepticality listener and friend of the blog Jeff Schwartz sent us a story describing his experience attending a Journey concert at a large complex with two friends. One of those friends, Michelle, had driven them all to the concert.

After the concert was over and the three friends left the stadium along with all of the other concertgoers, they realized that none of them had made a mental note of where they had parked the car. Jeff told us, “Michelle was getting seriously frustrated and was on the verge of tears. At one point, after searching the parking lot for over an hour, she sat down on the hood of a car, slammed her hand down on it and sobbed, in a tearful voice, “I can’t find my car anywhere! I’ll never find it! I’ve looked everywhere”

“With that,” he said, “I looked at her full in the face and said, ‘Michelle, perhaps you should start by looking under your hand.’ Miraculously, the car she chose to have her temper tantrum on, was her own misplaced car.”

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 269. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

This is, of course, not a miracle. I think most people have experienced the frustration of parking at a large venue and not remembering where. I have spent around an hour looking for my car on at least two occasions, so I can vouch for just how frustrating it can be. Cars also tend to look different at night, even when parking lots are lit, which aggravates the situation. Chances are actually very good that the group saw the car at least once and did not recognize it. So what are the chances that a frustrated driver collapses near their own car? Well, it depends on the number of cars in the lot at that time, which would be greatly reduced from an hour earlier. But another thing to consider is that this is one of those cases in which you find something in the last place you look.

A couple of nights ago I visited an emergency room to check an injury my son received in a high school lacrosse game and we witnessed a very, very frustrated woman throw a bit of a tantrum in the waiting room over a blanket she didn’t receive. She stated that she had been waiting for 5 hours, and while I have no way of knowing if that was true, it seemed like one of those crazy coincidences that her name was called 10 minutes after she gave up and left. However, it is not crazy. Her name was going to be called at some point, and the longer she stayed, the greater the chances were that it would be called shortly after she left. The same is true in this case — that they were bound to find her car eventually. The longer they looked, the more likely it would be found shortly after she became frustrated enough to express her emotions, especially since the longer they looked, the fewer cars there were in the lot.

So, while it is interesting that Michelle sat on a car that happened to be her own, especially without noticing, consider the keys you spent an hour looking for, only to find them in plain sight. Is it a crazy coincidence that they were where you found them?

Last week, I was at physical therapy and they were playing an instrumental song during my session. I remember thinking that the accordion reminded me of a song from a commercial from several years ago. I really liked that song and hadn’t heard it since then, but I couldn’t remember the lyrics or which ad it was in, and humming into those song ID apps doesn’t seem to work for me, so I figured I may never be able to purchase that great song for myself.

After my PT session, I got in my car and had my XM Sirius radio playing. Only a few minutes into my drive, what do you know? The song came on! It was “This Is The Day” by The The. I listen to that station all the time and hadn’t heard it before, but they just so happened to play it the day I thought about it.

What are the odds? It’s definitely the same song I was thinking of and not just me believing it was due to the timing. I remembered the melody of the song, the singer’s voice, and the instrumentation. And the accordion. 🙂

To add to that, the song’s lyrics are “This is the day your life will surely change” so that made me even more excited about finding out the song title and artist.

Oh, and I found the ad it was in. M&Ms 2007.

Thanks!

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 268. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

There is no way to know the odds of this happening without knowing how often the song is was played at the time. It is possible that the song was played often on that channel and just went unnoticed by the author, however, given that it’s not a Billboard hit, at least not in the U.S., I’d say the odds are pretty low.

If we knew how often the song was played, we could estimate the odds that the song would play at a specific point in time, giving us a better idea of the odds that she would hear it immediately following her physical therapy session.

Today during my 7 year old’s violin lesson, I was reading a “Mr. Men” book to my 4 year old. He had selected it randomly from the teacher’s complete set of the books.

I had just finished a page which mentioned “Mrs. Twinkle”, when my daughter started playing “Twinkle Twinkle Little Star”.

It wasn’t as a direct result of my reading – she was working her way backwards through her repertoire of pieces, so that had been set in motion before I’d even started reading the book. And there was nothing to specifically draw my son to this book.

I often notice that I’m reading a word at about the same time I hear somebody say it, but that easily make sense considering the number of words I read. But my daughter only knows about 6 violin pieces by heart!

So what are the odds?

Below are the extended notes provided by mathematician Brian Pasko for use in Skepticality Episode 267. Brian is on the faculty at a university in the southwestern United States. His interests include scientific skepticism, popular science books and improbable coincidences that makes one wonder just what the fates are up to. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

What a lovely vision: a young mother dramatically reading to the toddler in her lap while her daughter struggles through the elementary musical cannon. I can only hope that afternoon sunlight was streaming through the large windows of the studio…

How probable was your experience? I would say rather high! Of course, what questions we ask determines our estimate of the probability. Let’s start this way: the probability that a children’s book contains the word twinkle, fairly high; the probability that at some point during the lesson your seven year old daughter plays Twinkle, Twinkle Little Star I would say pretty close to one. (Probability is measured between zero and one with zero being cannot happen and one being cannot not happen.) In this case your experience is not that hard to believe.

Or, we could wonder what the probability is of reading a book with a character Miss Spider, Mr. Farmer, Ms. Wheels or, Madame Spaghetti (atop or otherwise) and noticing that your daughter plays one of the corresponding songs. In this case, your coincidence is even expected.

We can be a bit more specific, though we have to make some assumptions. There are numerous titles in the Mr. Men series but a box set of 50 books was issued in 2010, let’s suppose your son picked the book you read from one of these. I have been unable to determine the number of these books that include the character Mrs. Twinkle but let’s just assume two. (Yes, a bit arbitrary but it seems unlikely that she appears in only one title; if she is a regular character in the series, I expect a Google search would turn up some mention of her.) Twinkle, Twinkle Little Star takes about 30 seconds to play. Reading a Mr. Men book takes about 10 minutes and if the words ‘Mrs. Twinkle’ appears on three pages there is a 2 minute window that you could read the words ‘Mrs. Twinkle’ while your daughter is playing the song.

I wrote a short computer program to model the situation assuming the lesson was thirty minutes long. It turns out that the probability that you read the words “Mrs. Twinkle” while your daughter was playing Twinkle, Twinkle Little Star is about 0.27. Since two of the 50 books your son could have chosen include this character, I estimate the probability of your experience around 1.1%.

So, I think your improbable event is not all that improbable. Imagine the alternative: that one chooses a children’s book that does not have some similarity to a common children’s song.

We immigrated to Canada in 1981, settling in a small northern town, Fort St. John, British Columbia. There we met a person that my wife knew had been a friend of her Grandfather’s in the early 1930s in Germany, close to the town where she was born, and who had emigrated unbeknown to her sometime in the mid fifties to Canada, first moving to Vancouver Island and later to the same town where we finally settled. He and his wife became friends of ours. Now, that is not too crazy.

This year we decided to leave Canada and retire to the Azore Islands, where we met a friend of my sister’s – she has a house there and that is why we decided to move to the Azores – who lives close by, having had settled there coming from Germany in the mid eighties. He also coincidentally had been living previously close to the town where my wife was born.

On a visit with this gentleman this fall we met a German who hails from Berlin and now lives in Spain, a sailor who in the beginning of the eighties had sailed with his wife to Canada, where he stayed for half a year on Vancouver Island.

During the conversation when the sailor told us of his travels, he mentioned the name of our friend, that he had died two years previous and learned of that fact when he had visited Vancouver Island and tried to look him up.

He also told us that at the time when he came the first time to Vancouver Island he met the friend of my wife’s grandfather, a short while before that friend had decided to move north.

So on an island in the middle of the Atlantic we meet someone who knew someone who was a friend of ours who had lived several thousand kilometers away in the same town we once had lived in. What are the odds?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 266. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

One thing I noticed from this story is that everyone is German. This is not an irrelevant bit of information, since people tend to bond over things like sharing a country of origin, and immigrants also tend to cluster geographically.

So while the odds of this happening might be quite small, they aren’t as small as one might think. There’s a reason that the saying “It’s a small world” exists, and it’s not because the world is indeed small.

A few years ago, I began working for OKC Animal Welfare. The day I was released to work in the kennels, I was helping a citizen look for her dog, and was trying to explain the process.

The shelter has 5 rooms for dogs, divided by age, size, if they’re adoptable or not, and if they’re involved in a case. I took her into the first room, which was normally reserved for dogs under 6 months, and I pulled the first cage card we came to and explained what she needed to do if she found her dog.

As I put the card back, she looked into the kennel, looked at me and said “That’s my dog!”, which turned out to be an older border collie looking dog, so it shouldn’t have been in that room in the first place, and it’s stray time was up. (Luckily, they were going to try and place it in the adoption program, otherwise she would never have found it.)

At the time, in 2007, the shelter took in around 35 to 38,000 animals a year (roughly half of them dogs), the shelter probably held around 200-300 dogs that day (that’s the general average) and the human population of Oklahoma City was 546,000.

As well, a large percent of the dogs in the shelter never made it to adoption due to various factors, including temperament, health, and space. Another consideration is that probably only 10% of loose dogs are reported or come into the shelter.

Given that roughly 100-300 people came into the shelter a day, and they get nearly as many animals a day, what are the odds of finding a specific person’s dog in the first kennel on my first day in the shelter?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 265. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

Only a few pieces of information are needed to estimate the odds the way the author framed the question, but the author does not provide the most important: the odds that a specific dog would end up in the shelter. However, let’s pretend that the 10% mentioned answers that question. If there is a 1 in 10 chance that a dog would end up in the shelter, then there is a 1 in 10 chance that any given visitor’s dog will be found there. We must assume that if the dog is at the shelter, the owner will find it. It’s just a matter of when. Since there are 5 kennels, then we can multiply that probability by 1/5th to find the probability that a person’s dog will be found in the first kennel. That makes it .02 or 1 in 50 that the owner will find their dog and find it in the first kennel. In other words, as the question is framed, the odds are not crazy at all.

The number of people visiting the shelter and the number of dogs housed in it are irrelevant. No owner would just sample the dogs; they would want to do an exhaustive search of the shelter to find their dog. Likewise, the population of the town is irrelevant.

In May of this year I attended a conference of humanist organizations in Atlanta, Georgia where I had a conversation with one of the local organizers. She told me she had a brother who was living in Hawaii but considering a move to Los Angeles, where I live, sometime later in the year and asked if she could pass my phone number on to him.

I had forgotten about the exchange until last week when I got a call from an unknown 808 area code number. The young man on the other end of the line explained who he was and how he had my phone number. We chatted briefly and I found out he and his wife had arrived in LA, they were looking for a place to rent and we made a date for lunch with a couple days later.

As we got to know each other over lunch, I learned that they knew nothing of the organization his sister and I are both affiliated with, so I told him how it was I came to meet her. Then they asked about my family and I explained that I had two children, one not much different in age from them, who had graduated from a small college in Minnesota in 2014 with a degree in Classics.

The young woman interjected, “Your daughter didn’t happen to go to Carleton College, did she?” Which, if you’re listening to this podcast, you can already guess what my answer was. Listeners should understand that Carleton is a college of 2,000 students in rural Minnesota. This young woman explained that her childhood best friend from growing up in Houston, TX had graduated from Carleton the year before in 2013, also in Classics, a department of about a dozen students.

I texted my daughter and my lunch companion texted her childhood friend to ask if they knew each other only to find out that the two of them had been study buddies through ancient Greek language for the 3 years they overlapped and are still close friends.

And by this last weekend, they had found a place to live: they will be renting from my wife and me starting in a couple weeks.

Seriously? The odds of this must be crazy!

Below are the extended notes provided by statistician and podcaster Kyle Polich for use in Skepticality Episode 264. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

(Kyle studied computer science followed by artificial intelligence in grad school with a focus in probabilistic reasoning and planning. His general interests range from obvious areas like statistics, machine learning, data viz, and optimization to data provenance, data governance, econometrics, and metrology. He enjoys exploring the intersection of statistics and skepticism and sharing related insights with others including through his podcast Data Skeptic. Visit Kyle’s blog Data Skeptic, and give the podcast a listen.)

So this story covers a series of seemingly unlikely events. Let’s try and break them down and isolate the parts that are not surprising from the parts that are eyebrow raising.

One of the important lessons here is around *conditional* probability. What is the probability that a person can play “Mary Had a Little Lamb” on the bassoon? Pretty low! What about the probability of that given the fact that they’re a professional bassoon player – very high!

To begin with, our listener is out of town chatting with a conference organizer who mentions her brother is moving to the listener’s city. There are almost 40k municipalities in the United States, so shall we say the odds of this are 1 in 40k or 0.0025%? Not quite.

Let’s consider the complement of this situation. Imagine you meet someone and proudly announce “I’m from Los Angeles”, to which they reply, “Cool! I have a good friend that lives in Gainsville, FL!” I mean, that’s nice, but I’m from LA. I think it’s fair to say our investigation only starts *conditioned* on the fact that a common city comes up in conversation.

Moving ahead to the part of the story in which the listener meets the relocating young brother and wife, and mentions having a daughter who attended a small college in Minnesota in 2014 with a degree in classics. The young women mentions having a close childhood friend who studied the same subject in a Minnesota school, and asks if they might perhaps have attended the same school and know each other. There are almost 200 colleges and universities in Minnesota. I’m not sure what qualifies as small, but if half of them are considered small, we can call those odds about a 1% chance.

Setting aside how many childhood friends the young woman had and how many universities they spread out into, maybe we call these odds 1 in 100 chance. That’s like betting on a specific number for rulet and winning. Unlikely, but not extraordinary.

But now we get into *conditional* probability. What are the odds that two students at a small school in a small department of about a dozen students know each other? I should hope pretty high!

So all in all, I find this one noteworthy, but not excessively surprising, and if I had to put a firm number on it, I’d say in the neighborhood of 1% likelihood.

The US Census tracks state to state movement. Kyle put together a fun, interactive data visualization that allows people to select a state and see the percentage of people that leave that state and what other states they migrate to.

My first job after college sent me on a five-day training course in Boston, where I made fast friends with three other students. We were all traveling from different states (North Carolina, Nebraska, Michigan, & Missouri) and our ages ranged from 22 to mid 40s. Somehow we all hit it off in class and went to dinner every night before returning to our hotel.

Eight months later, I flew from NC to San Diego on a work conference. Checking into my hotel, I happened to bump into my Nebraska buddy hauling his luggage through the lobby. Amazed, we chatted for a few minutes, and I learned he was on a work trip of his own, unrelated to mine.

The next evening, I exited the elevator and passed none other than my Missouri friend, who was staying on my floor. He too was on a work trip, and after picking my jaw up from the carpet, I suggested we meet up with Nebraska guy and go out to dinner for old time’s sake. “What are the chances?” remained the theme of our conversation as we set off to find Mr. Nebraska.

Long story short, the three of us ended up at a seafood place, laughing, swapping stories, when suddenly our Michigan friend passed by our table, did a quadruple take, stared at us for a moment in silence, and burst out in laughter. Turned out he was a vendor at my conference, and was sent to demo a product that I would eventually take back to NC.

So, our impromptu gang had managed to assemble once again, from one coast to the other, from Massachusetts to California, eight months apart. I tell all my friends and dates this story, and none of them believe it. It’s certainly the most improbably bizarre event that’s ever happened to me, and I can’t even begin to calculate the odds.

You’d think I would’ve kept up with these guys, but honestly I never did. We never got together again after that fateful week in San Diego

Below are the extended notes provided by mathematician Brian Pasko for use in Skepticality Episode 263. Brian is on the faculty at Eastern New Mexico University. His interests include scientific skepticism, popular science books and improbable coincidences that makes one wonder just what the fates are up to. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

Cool! The Drake equation is named for physicist Frank Drake. It provides important considerations to estimate the probability of extraterrestrial civilizations in the universe. Finding the probability of you four friends meeting seems hard. Let’s analyze your situation with Drake as inspiration. The probability that you all meet as you described is the product of the probabilities that:

You all happen to be in the same city (or, nearby) at the same time;

three of you get the same hotel (and actually see each other!); and

that the third person comes to the restaurant at which the others are eating (and actually see each other!).

This product is, let’s say, small. However, there are some interesting facets that affect this probability. The first is that I suspect you four are in the same industry. This may increase the likelihood of you all being in the same area at the same time. If this assumption is correct, you’re all likely in the same economic class as well. This narrows the selection of hotels you each choose and the restaurants you’re likely to patronize.

You could have met Michigan and Nebraska at the hotel instead of Missouri and Nebraska. So we need only that three of the four friends were at the same hotel. This increases the likelihood of a meeting by factor of three! Also, you could have seen any of the other two at any time during the day. In addition, you’re all on work trips and so probably are moving in and out of your rooms at the same times of the day, which increases the likelihood of a meeting.

Of course, the meet up could have happened in a lot of different ways. For example, two pairs of you could have met at two different hotels; or not at hotels at all but on the street getting the same cab; or at a pub after work hours… You get the idea.

A consequence of Drake’s ideas is that if we happened to find alien life in our solar system it would imply that the universe is positively rife with life! I suggest that if such a meet up happens again between you four, rather than lightening striking twice, it means that you’re often in the same place at the same time and just don’t see each other.

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